Question 1

When the potential energy of a system is independent of time,the wave function of the system

Accepted Answer

A) is a constant. 
B) is directly proportional to the time. 
C) cannot be normalized. 
D) depends only on the center of mass,   ,of the system. 
E) depends on the vector positions,   i,of each particle in the system. 
A) is a constant. 
B) is directly proportional to the time. 
C) cannot be normalized. 
D) depends only on the center of mass,   ,of the system. 
E) depends on the vector positions,   i,of each particle in the system. E

Question 2

When a particle approaching a potential step has a total energy that is greater than the potential step,what is the probability that the particle will be reflected?

Accepted Answer

A) P  0. 
E) P = ∞. 
A) P  0. 
E) P = ∞. D

Question 3

A 15-kg mass,attached to a massless spring whose force constant is 2500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if En = nhf.

Accepted Answer

A) 1.5 × 1033 
B) 3.0 × 1033 
C) 4.5 × 1033 
D) 5.4 × 1033 
E) 1.0 × 1033 
A) 1.5 × 1033 
B) 3.0 × 1033 
C) 4.5 × 1033 
D) 5.4 × 1033 
E) 1.0 × 1033 A

Question 4

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg ⋅ m/s)?

Accepted Answer

A) 6.6 × 10−34 
B) 3.3 × 10−34 
C) 9.9 × 10−34 
D) 13 × 10−34 
E) cannot be solved unless mass of particle is known 
A) 6.6 × 10−34 
B) 3.3 × 10−34 
C) 9.9 × 10−34 
D) 13 × 10−34 
E) cannot be solved unless mass of particle is known

Question 5

The graph below represents a wave function ψ(x)for a particle confined to −4.00 m ≤ x ≤ +4.00 m.The magnitude of the normalization constant A is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E) 4. 
A)    . 
B)    . 
C)    . 
D)    . 
E) 4.

Question 6

The expectations value of a function f(x)of x when the wave function depends only on x is given by  =

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 7

Frank says that quantum mechanics does not apply to baseballs because they do not jump from quantum state to quantum state when being thrown.Francine agrees with him.She says that there is no uncertainty in a baseball's position or momentum.Are they correct,or not,and why?

Accepted Answer

A) They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives.Therefore we cannot determine whether or not there is uncertainty in its position or momentum. 
B) They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives.Therefore its position and momentum are completely uncertain until it is caught. 
C) They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions.The uncertainties in its position and momentum are too small to observe. 
D) They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions.Because of the number of transitions its position and momentum are completely uncertain until it is caught. 
E) Quantum mechanics states that they are correct as long as they do not make any observations,but wrong as soon as they begin to make observations. 
A) They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives.Therefore we cannot determine whether or not there is uncertainty in its position or momentum. 
B) They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives.Therefore its position and momentum are completely uncertain until it is caught. 
C) They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions.The uncertainties in its position and momentum are too small to observe. 
D) They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions.Because of the number of transitions its position and momentum are completely uncertain until it is caught. 
E) Quantum mechanics states that they are correct as long as they do not make any observations,but wrong as soon as they begin to make observations.

Question 8

The graph below represents a wave function ψ(x)for a particle confined to −2.00 m ≤ x ≤ +2.00 m.The value of the normalization constant A may be

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E) either   or   . 
A)    . 
B)    . 
C)    . 
D)    . 
E) either   or   .

Question 9

Calculate the ground state energy (in eV)for an electron in a box (an infinite well)having a width of 0.050 nm.

Accepted Answer

A) 10 
B) 75 
C) 24 
D) 150 
E) 54 
A) 10 
B) 75 
C) 24 
D) 150 
E) 54

Question 10

The ground state energy of a harmonic oscillator is

Accepted Answer

A)    
B)    
C)    
D) E = 0 
E)    
A)    
B)    
C)    
D) E = 0 
E)

Question 11

The average position,or expectation value,of a particle whose wave function ψ(x)depends only on the value of x,is given by  =

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 12

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

Accepted Answer

A) 1 
B) 4 
C) 2 
D) 8 
E) 16 
A) 1 
B) 4 
C) 2 
D) 8 
E) 16

Question 13

The wave function ψ(x)of a particle confined to 0 ≤ x ≤ L is given by ψ(x)= Ax.ψ(x)= 0 for x  L.When the wave function is normalized,the probability density at coordinate x has the value

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 14

A particle in a finite potential well has energy E,as shown below.  
The wave function in region I where x I =

Accepted Answer

A) Ae−Cx. 
B) AeCx. 
C) F sin kx. 
D) G cos kx. 
E) F sin kx + G cos kx. 
A) Ae−Cx. 
B) AeCx. 
C) F sin kx. 
D) G cos kx. 
E) F sin kx + G cos kx.

Question 15

The wave function for a particle in a one-dimensional box is  
)Which statement is correct?

Accepted Answer

A) This wavefunction gives the probability of finding the particle at x. 
B) |Ψ(x)|2 gives the probability of finding the particle at x. 
C) |Ψ(x)|2 Δx gives the probability of finding the particle between x and x + Δx. 
D)    gives the probability of finding the particle at a particular value of x. 
E)    gives the probability of finding the particle between x and x + Δx. 
A) This wavefunction gives the probability of finding the particle at x. 
B) |Ψ(x)|2 gives the probability of finding the particle at x. 
C) |Ψ(x)|2 Δx gives the probability of finding the particle between x and x + Δx. 
D)    gives the probability of finding the particle at a particular value of x. 
E)    gives the probability of finding the particle between x and x + Δx.

Question 16

Classically,the concept of "tunneling" is impossible.Why?

Accepted Answer

A) The kinetic energy of the particle would be negative. 
B) The velocity of the particle would be negative. 
C) The total energy of a particle is equal to the kinetic and potential energies. 
D) The kinetic energy must be equal to the potential energy. 
E) The total energy for the particle would be negative. 
A) The kinetic energy of the particle would be negative. 
B) The velocity of the particle would be negative. 
C) The total energy of a particle is equal to the kinetic and potential energies. 
D) The kinetic energy must be equal to the potential energy. 
E) The total energy for the particle would be negative.

Question 17

A physically reasonable wave function,ψ(x),for a one-dimensional system must

Accepted Answer

A) be defined at all points in space. 
B) be continuous at all points in space. 
C) be single-valued. 
D) obey all the constraints listed above. 
E) obey only (b)and (c)above. 
A) be defined at all points in space. 
B) be continuous at all points in space. 
C) be single-valued. 
D) obey all the constraints listed above. 
E) obey only (b)and (c)above.

Question 18

A particle in a finite potential well has energy E,as shown below.  
The wave function in region III where x > L has the form ψIII =

Accepted Answer

A) Ae−Cx. 
B) AeCx. 
C) F sin kx. 
D) G cos kx. 
E) F sin kx + G cos kx. 
A) Ae−Cx. 
B) AeCx. 
C) F sin kx. 
D) G cos kx. 
E) F sin kx + G cos kx.

Question 19

Quantum tunneling occurs in

Accepted Answer

A) nuclear fusion. 
B) radioactive decay by emission of alpha particles. 
C) the scanning tunneling microscope. 
D) all of the above. 
E) only (b)and (c)above. 
A) nuclear fusion. 
B) radioactive decay by emission of alpha particles. 
C) the scanning tunneling microscope. 
D) all of the above. 
E) only (b)and (c)above.

Question 20

A particle has a total energy that is less than that of a potential barrier.When the particle penetrates the barrier,its wave function is

Accepted Answer

A) a positive constant. 
B) exponentially increasing. 
C) oscillatory. 
D) exponentially decreasing. 
E) none of the above. 
A) a positive constant. 
B) exponentially increasing. 
C) oscillatory. 
D) exponentially decreasing. 
E) none of the above.

Exam 41: Quantum Mechanics

When the potential energy of a system is independent of time,the wave function of the system

When a particle approaching a potential step has a total energy that is greater than the potential step,what is the probability that the particle will be reflected?

A 15-kg mass,attached to a massless spring whose force constant is 2500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if En = nhf.

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg ⋅ m/s)?

The graph below represents a wave function ψ(x)for a particle confined to −4.00 m ≤ x ≤ +4.00 m.The magnitude of the normalization constant A is

The expectations value of a function f(x)of x when the wave function depends only on x is given by < f(x)> =

Frank says that quantum mechanics does not apply to baseballs because they do not jump from quantum state to quantum state when being thrown.Francine agrees with him.She says that there is no uncertainty in a baseball's position or momentum.Are they correct,or not,and why?

The graph below represents a wave function ψ(x)for a particle confined to −2.00 m ≤ x ≤ +2.00 m.The value of the normalization constant A may be

Calculate the ground state energy (in eV)for an electron in a box (an infinite well)having a width of 0.050 nm.

The ground state energy of a harmonic oscillator is

The average position,or expectation value,of a particle whose wave function ψ(x)depends only on the value of x,is given by < x > =

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

The wave function ψ(x)of a particle confined to 0 ≤ x ≤ L is given by ψ(x)= Ax.ψ(x)= 0 for x < 0 and x > L.When the wave function is normalized,the probability density at coordinate x has the value

A particle in a finite potential well has energy E,as shown below. The wave function in region I where x < 0 has the form ψI =

The wave function for a particle in a one-dimensional box is )Which statement is correct?

Classically,the concept of "tunneling" is impossible.Why?

A physically reasonable wave function,ψ(x),for a one-dimensional system must

A particle in a finite potential well has energy E,as shown below. The wave function in region III where x > L has the form ψIII =

Quantum tunneling occurs in

A particle has a total energy that is less than that of a potential barrier.When the particle penetrates the barrier,its wave function is

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A 15-kg mass,attached to a massless spring whose force constant is 2500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if E_n = nhf.

A particle in a finite potential well has energy E,as shown below. The wave function in region I where x < 0 has the form ψ_I =

A particle in a finite potential well has energy E,as shown below. The wave function in region III where x > L has the form ψ_III =